Before the Civil War, the parties (and especially the Democratic-Republicans) often nominated presidential candidates wealthy in land and slaves. George Washington, Thomas Jefferson, James Madison, Andrew Jackson, and John Tyler were some of the richest men of the young Republic. But since 1865, it has become unusual for parties to nominate very wealthy men.
I can think of only five very rich post-1865 presidential nominees: John McCain, John Kerry, John F. Kennedy, Herbert Hoover and Samuel Tilden.
Strikingly, only two of the five—Hoover and Tilden—made their money themselves.
(James Cox, the Democratic nominee in 1920, proceeded to become very rich after running for president. The two Roosevelts were born to wealth, but had lost much of their fortune by the time they gained the presidency. Definitions of "very wealthy" are maybe inescapably arbitrary, but neither of the George Bushes would seem to me to qualify at the time he won the presidency.)
In that sense, Mitt Romney is defying what seems to be a strong American current.
If he wins against that current, it may be because his two severest critics, Rick Perry and Newt Gingrich, are not only hardly poor, but both made their money in ways that you might have thought even more ethically disturbing than Romney's: in Perry's case, a series of very cozy land deals; in Gingrich's case, by lobbying in all but name.